An adjoint based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill-posed stochastic inverse problem is restated as a conditionally well-posed L2 optimization problem. The gradient...

Initial condition inverse problems are ill-posed and computationally expensive to solve. We present a computational approach for solving inverse problems in the realm of onedimensional contaminant transport. The approach employs finite differencing as a forward solver and probabilistic methods for inversion. Markov Chain Monte Carlo sampling is used to efficiently recover posterior probabilitie...

Regularization is an well-known technique for obtaining stable solution of ill-posed inverse problems. In this paper we establish a key relationship among the regularization methods with an edge-preserving noise filtering method which leads to an efficient adaptive regularization methods. We show experimentally the efficiency and superiority of the proposed regularization methods for some inver...

Inversion of MT data is an inherently nonunique and unstable problem due to the ill-posedness of the electromagnetic inverse problem. A variety of models may fit the data very well. To overcome this illposed nature of the inverse problem, we use Tikhonov’s regularization in which the ill-posed problem is replaced by a family of well-posed problems. We also analyze the behavior of the Tikhonov r...

We present an error analysis for the numerical diierentiation of noisy data via smoothing cubic splines. Our treatment is elementary enough to be included in a course on numerical analysis. Still, it accounts for all numerical problems that arise in the solution of much more complex ill-posed inverse problems.